相关论文: TBA type equations and tropical curves

We reconcile the discrepancy between the complex and tropical counts of some enumerative problems reducing to positive characteristic. Each problem that we consider suggests a prime with special behaviour. Modulo this prime, the solutions…

In arXiv:0908.4052, Nekrasov and Shatashvili pointed out that the N=2 instanton partition function in a special limit of the Omega-deformation parameters is characterized by certain thermodynamic Bethe ansatz (TBA) like equations. In this…

Suppose X is a (smooth projective irreducible algebraic) curve over a finite field k. Counting the number of points on X over all finite field extensions of k will not determine the curve uniquely. Actually, a famous theorem of Tate implies…

We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized $T\bar T$ deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic…

We propose a generalization of tropical curves by dropping the rationality and integrality requirements while preserving the balancing condition. An interpretation of such curves as critical points of a certain quadratic functional allows…

We show how a lattice approach can be used to derive Thermodynamic Bethe Ansatz (TBA) equations describing all excitations for boundary flows. The method is illustrated for a prototypical flow of the tricritical Ising model by considering…

Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are…

This paper is the first part in a series of three papers devoted to the study of enumerative invariants of abelian surfaces through the tropical approach. In this paper, we consider the enumeration of genus $g$ curves of fixed degree…

We propose an exact summation method to compute thermodynamic observables in integrable quantum field theories. The key idea is to use the matrix-tree theorem to write the Gaudin determinants that appear in the cluster expansion as a sum…

We investigate the thermodynamic Bethe ansatz (TBA) equations for a system of particles which dynamically interacts via the scattering matrix of affine Toda field theory and whose statistical interaction is of a general Haldane type. Up to…

We study the deformed supersymmetric quantum mechanics with a polynomial superpotential with $\hbar$ correction. In the minimal chamber, where all turning points are real and distinct, it was shown that the exact Wentzel--Kramers--Brillouin…

We enumerate rational curves in toric surfaces passing through points and satisfying cross-ratio constraints using tropical and combinatorial methods. Our starting point is arXiv:1509.07453, where a tropical-algebraic correspondence theorem…

The thermodynamic Bethe ansatz (TBA) and the excited state TBA equations for an integrable spin chain related to the Lie superalgebra osp(1|2) are proposed by the quantum transfer matrix (QTM) method. We introduce the fusion hierarchy of…

We consider the tricritical Ising model on a strip or cylinder under the integrable perturbation by the thermal $\phi_{1,3}$ boundary field. This perturbation induces five distinct renormalization group (RG) flows between Cardy type…

We consider the critical non-unitary minimal model {\cal M}(3,5) with integrable boundaries. We analyze the patterns of zeros of the eigenvalues of the transfer matrix and then determine the spectrum of the critical theory through the…

(R-channel) TBA is elaborated to find the effective central charge dependence on the boundary parameters for the massless boundary sine-Gordon model with the coupling constant $(8\pi) /\beta^2 = 1+ \lambda $ with $\lambda$ a positive…

In this paper, second installment in a series of three, we give a correspondence theorem to relate the count of genus $g$ curves in a fixed linear system in an abelian surface to a tropical count. To do this, we relate the linear system…

We describe a modified transfer matrix renormalization group (TMRG) algorithm and apply it to calculate thermodynamic properties of the one-dimensional t-J model. At the supersymmetric point we compare with Bethe ansatz results and make…

We give a rigorous treatment to the thermodynamic limit of the 6-vertex model. We prove that the unique solution of the Bethe-Ansatz equation exists and the distribution of the roots converges to a continuum measure. We solve this problem…

We present a multi-grid algorithm in order to solve numerically the thermodynamic Bethe ansatz equations. We specifically adapt the program to compute the data of the conformal field theory reached in the ultraviolet limit. Submitted to…